The　dynamic　snap-through　phenomena　and　nonlinear　vibrations　with　two　potential　wells　are　investigated　for　a　bistable　asymmetric　cross-ply　composite-laminated　square　plates.　The　center　of　the　plate　is　fixed　supported.　The　four　edges　of　the　plate　are　free.　A　base　excitation　is　given　at　the　center　of　the　plates.　The　Hamilton＇s　principle　is　employed　to　establish　the　partial　differential　governing　equations　of　motions　for　the　bistable　plates.　Three　equilibrium　configurations　corresponding　to　two　stable　configurations　and　one　unstable　configuration　can　be　determined　by　solving　the　nonlinear　static　equations.　The　static　bifurcation　diagrams　are　obtained,　of　which　the　type　is　super-critical　pitchfork　bifurcation.　Absolute　value　of　critical　temperature　difference　of　bifurcation　increases　with　the　increase　of　the　quantity　of　layers.　Two　energy　potential　wells　are　determined　based　on　two　stable　configurations.　The　potential　energy　curves　are　determined.　The　potential　curve　consists　of　two　potential　wells　and　one　potential　barrier.　Threshold　that　is　the　difference　between　the　maximum　value　and　the　minimum　value　of　the　potential　energy　curve　adds　with　the　adding　of　the　quantity　of　layers.　The　influence　of　the　base　excitation　amplitude　on　the　dynamic　snap-through　phenomena　and　nonlinear　vibrations　is　studied.　The　dynamic　snap-through　occurs　accompanying　with　the　periodic　vibration,　the　quasi-periodic　vibration　and　the　chaotic　vibration　in　the　dynamic　environments.